LMFDB - Embedded newform 1110.2.l.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} -0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075i q^{13} +(2.75974 + 2.75974i) q^{14} +(2.23398 + 0.0966903i) q^{15} +1.00000 q^{16} -7.07368 q^{17} +1.00000 q^{18} +(-2.01227 + 2.01227i) q^{19} +(1.51129 + 1.64803i) q^{20} +3.90286i q^{21} +0.350472 q^{22} -1.24836i q^{23} +(0.707107 + 0.707107i) q^{24} +(-0.432008 + 4.98130i) q^{25} -3.27075 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.75974 + 2.75974i) q^{28} +(-6.14644 - 6.14644i) q^{29} +(-0.0966903 + 2.23398i) q^{30} +(-2.76854 + 2.76854i) q^{31} +1.00000i q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-8.71889 - 0.377368i) q^{35} +1.00000i q^{36} +(-4.91116 + 3.58895i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(-2.31277 - 2.31277i) q^{39} +(-1.64803 + 1.51129i) q^{40} +5.57830i q^{41} -3.90286 q^{42} +3.23195i q^{43} +0.350472i q^{44} +(-1.64803 + 1.51129i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.23228i q^{49} +(-4.98130 - 0.432008i) q^{50} +(5.00185 - 5.00185i) q^{51} -3.27075i q^{52} +(-3.45760 - 3.45760i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.577588 + 0.529665i) q^{55} +(-2.75974 - 2.75974i) q^{56} -2.84578i q^{57} +(6.14644 - 6.14644i) q^{58} +(-10.6205 + 10.6205i) q^{59} +(-2.23398 - 0.0966903i) q^{60} +(1.30384 - 1.30384i) q^{61} +(-2.76854 - 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} -1.00000 q^{64} +(5.39030 - 4.94305i) q^{65} +(-0.247821 + 0.247821i) q^{66} +(-10.6169 - 10.6169i) q^{67} +7.07368 q^{68} +(0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} -1.00000 q^{72} +(-0.998067 + 0.998067i) q^{73} +(-3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 - 2.01227i) q^{76} +(-0.967210 - 0.967210i) q^{77} +(2.31277 - 2.31277i) q^{78} +(-2.47200 + 2.47200i) q^{79} +(-1.51129 - 1.64803i) q^{80} -1.00000 q^{81} -5.57830 q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(10.6904 + 11.6576i) q^{85} -3.23195 q^{86} +8.69238 q^{87} -0.350472 q^{88} +(-3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 + 9.02641i) q^{91} +1.24836i q^{92} -3.91530i q^{93} +(5.76291 + 5.76291i) q^{94} +(6.35741 + 0.275159i) q^{95} +(-0.707107 - 0.707107i) q^{96} +7.94277 q^{97} +8.23228 q^{98} -0.350472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) $ 36 * q - 36 * q^4 + 4 * q^7	$ 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−1.51129	−	1.64803i	−0.675869	−	0.737022i
$5$	−1.51129	−	1.64803i	−0.675869	−	0.737022i
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	2.75974	−	2.75974i	1.04308	−	1.04308i	0.0440528	−	0.999029i	$-0.485973\pi$
$7$	2.75974	−	2.75974i	1.04308	−	1.04308i	0.999029	−	0.0440528i	$-0.0140270\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	1.64803	−	1.51129i	0.521153	−	0.477912i
$11$		−	0.350472i		−	0.105671i	−0.998603	−	0.0528356i	$-0.983174\pi$
$11$		−	0.350472i		−	0.105671i	0.998603	−	0.0528356i	$-0.0168259\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$			3.27075i			0.907143i	0.891220	+	0.453572i	$0.149850\pi$
$13$			3.27075i			0.907143i	−0.891220	+	0.453572i	$0.850150\pi$
$14$	2.75974	+	2.75974i	0.737570	+	0.737570i
$15$	2.23398	+	0.0966903i	0.576810	+	0.0249653i
$16$	1.00000			0.250000
$17$	−7.07368			−1.71562			−0.857810	−	0.513967i	$-0.828176\pi$
$17$	−7.07368			−1.71562			−0.857810	+	0.513967i	$0.828176\pi$
$18$	1.00000			0.235702
$19$	−2.01227	+	2.01227i	−0.461647	+	0.461647i	−0.899195	−	0.437548i	$-0.855847\pi$
$19$	−2.01227	+	2.01227i	−0.461647	+	0.461647i	0.437548	+	0.899195i	$0.355847\pi$
$20$	1.51129	+	1.64803i	0.337935	+	0.368511i
$21$			3.90286i			0.851673i
$22$	0.350472			0.0747209
$23$		−	1.24836i		−	0.260301i	−0.991494	−	0.130150i	$-0.958454\pi$
$23$		−	1.24836i		−	0.260301i	0.991494	−	0.130150i	$-0.0415460\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	−0.432008	+	4.98130i	−0.0864015	+	0.996260i
$26$	−3.27075			−0.641447
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.75974	+	2.75974i	−0.521541	+	0.521541i
$29$	−6.14644	−	6.14644i	−1.14137	−	1.14137i	−0.988201	−	0.153165i	$-0.951053\pi$
$29$	−6.14644	−	6.14644i	−1.14137	−	1.14137i	−0.153165	−	0.988201i	$-0.548947\pi$
$30$	−0.0966903	+	2.23398i	−0.0176532	+	0.407866i
$31$	−2.76854	+	2.76854i	−0.497244	+	0.497244i	−0.910579	−	0.413335i	$-0.864364\pi$
$31$	−2.76854	+	2.76854i	−0.497244	+	0.497244i	0.413335	+	0.910579i	$0.364364\pi$
$32$			1.00000i			0.176777i
$33$	0.247821	+	0.247821i	0.0431401	+	0.0431401i
$34$		−	7.07368i		−	1.21313i
$35$	−8.71889	−	0.377368i	−1.47376	−	0.0637869i
$36$			1.00000i			0.166667i
$37$	−4.91116	+	3.58895i	−0.807389	+	0.590019i
$37$	−4.91116	+	3.58895i	−0.807389	+	0.590019i
$38$	−2.01227	−	2.01227i	−0.326433	−	0.326433i
$39$	−2.31277	−	2.31277i	−0.370340	−	0.370340i
$40$	−1.64803	+	1.51129i	−0.260576	+	0.238956i
$41$			5.57830i			0.871185i	0.900144	+	0.435592i	$0.143461\pi$
$41$			5.57830i			0.871185i	−0.900144	+	0.435592i	$0.856539\pi$
$42$	−3.90286			−0.602224
$43$			3.23195i			0.492868i	0.969160	+	0.246434i	$0.0792588\pi$
$43$			3.23195i			0.492868i	−0.969160	+	0.246434i	$0.920741\pi$
$44$			0.350472i			0.0528356i
$45$	−1.64803	+	1.51129i	−0.245674	+	0.225290i
$46$	1.24836			0.184060
$47$	5.76291	−	5.76291i	0.840606	−	0.840606i	−0.148331	−	0.988938i	$-0.547390\pi$
$47$	5.76291	−	5.76291i	0.840606	−	0.840606i	0.988938	+	0.148331i	$0.0473902\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		−	8.23228i		−	1.17604i
$50$	−4.98130	−	0.432008i	−0.704462	−	0.0610951i
$51$	5.00185	−	5.00185i	0.700399	−	0.700399i
$52$		−	3.27075i		−	0.453572i
$53$	−3.45760	−	3.45760i	−0.474938	−	0.474938i	0.428571	−	0.903508i	$-0.359017\pi$
$53$	−3.45760	−	3.45760i	−0.474938	−	0.474938i	−0.903508	+	0.428571i	$0.859017\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	−0.577588	+	0.529665i	−0.0778820	+	0.0714200i
$56$	−2.75974	−	2.75974i	−0.368785	−	0.368785i
$57$		−	2.84578i		−	0.376933i
$58$	6.14644	−	6.14644i	0.807068	−	0.807068i
$59$	−10.6205	+	10.6205i	−1.38267	+	1.38267i	−0.542832	+	0.839841i	$0.682648\pi$
$59$	−10.6205	+	10.6205i	−1.38267	+	1.38267i	−0.839841	+	0.542832i	$0.817352\pi$
$60$	−2.23398	−	0.0966903i	−0.288405	−	0.0124827i
$61$	1.30384	−	1.30384i	0.166940	−	0.166940i	−0.618693	−	0.785633i	$-0.712338\pi$
$61$	1.30384	−	1.30384i	0.166940	−	0.166940i	0.785633	+	0.618693i	$0.212338\pi$
$62$	−2.76854	−	2.76854i	−0.351605	−	0.351605i
$63$	−2.75974	−	2.75974i	−0.347694	−	0.347694i
$64$	−1.00000			−0.125000
$65$	5.39030	−	4.94305i	0.668584	−	0.613110i
$66$	−0.247821	+	0.247821i	−0.0305047	+	0.0305047i
$67$	−10.6169	−	10.6169i	−1.29707	−	1.29707i	−0.930322	−	0.366744i	$-0.880473\pi$
$67$	−10.6169	−	10.6169i	−1.29707	−	1.29707i	−0.366744	−	0.930322i	$-0.619527\pi$
$68$	7.07368			0.857810
$69$	0.882722	+	0.882722i	0.106267	+	0.106267i
$70$	0.377368	−	8.71889i	0.0451041	−	1.04211i
$71$	15.8980			1.88675			0.943373	−	0.331733i	$-0.107633\pi$
$71$	15.8980			1.88675			0.943373	+	0.331733i	$0.107633\pi$
$72$	−1.00000			−0.117851
$73$	−0.998067	+	0.998067i	−0.116815	+	0.116815i	−0.763098	−	0.646283i	$-0.776323\pi$
$73$	−0.998067	+	0.998067i	−0.116815	+	0.116815i	0.646283	+	0.763098i	$0.276323\pi$
$74$	−3.58895	−	4.91116i	−0.417207	−	0.570910i
$75$	−3.21684	−	3.82779i	−0.371448	−	0.441995i
$76$	2.01227	−	2.01227i	0.230823	−	0.230823i
$77$	−0.967210	−	0.967210i	−0.110224	−	0.110224i
$78$	2.31277	−	2.31277i	0.261870	−	0.261870i
$79$	−2.47200	+	2.47200i	−0.278122	+	0.278122i	−0.832359	−	0.554237i	$-0.813010\pi$
$79$	−2.47200	+	2.47200i	−0.278122	+	0.278122i	0.554237	+	0.832359i	$0.313010\pi$
$80$	−1.51129	−	1.64803i	−0.168967	−	0.184255i
$81$	−1.00000			−0.111111
$82$	−5.57830			−0.616020
$83$	−10.6094	−	10.6094i	−1.16454	−	1.16454i	−0.983471	−	0.181065i	$-0.942046\pi$
$83$	−10.6094	−	10.6094i	−1.16454	−	1.16454i	−0.181065	−	0.983471i	$-0.557954\pi$
$84$		−	3.90286i		−	0.425836i
$85$	10.6904	+	11.6576i	1.15954	+	1.26445i
$86$	−3.23195			−0.348510
$87$	8.69238			0.931921
$88$	−0.350472			−0.0373604
$89$	−3.03601	−	3.03601i	−0.321816	−	0.321816i	0.527647	−	0.849464i	$-0.323074\pi$
$89$	−3.03601	−	3.03601i	−0.321816	−	0.321816i	−0.849464	+	0.527647i	$0.823074\pi$
$90$	−1.51129	−	1.64803i	−0.159304	−	0.173718i
$91$	9.02641	+	9.02641i	0.946225	+	0.946225i
$92$			1.24836i			0.130150i
$93$		−	3.91530i		−	0.405998i
$94$	5.76291	+	5.76291i	0.594398	+	0.594398i
$95$	6.35741	+	0.275159i	0.652256	+	0.0282308i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	7.94277			0.806466			0.403233	−	0.915097i	$-0.367886\pi$
$97$	7.94277			0.806466			0.403233	+	0.915097i	$0.367886\pi$
$98$	8.23228			0.831586
$99$	−0.350472			−0.0352238
$100$	0.432008	−	4.98130i	0.0432008	−	0.498130i
$101$			0.514124i			0.0511573i	0.999673	+	0.0255786i	$0.00814282\pi$
$101$			0.514124i			0.0511573i	−0.999673	+	0.0255786i	$0.991857\pi$
$102$	5.00185	+	5.00185i	0.495257	+	0.495257i
$103$	−9.07861			−0.894542			−0.447271	−	0.894398i	$-0.647604\pi$
$103$	−9.07861			−0.894542			−0.447271	+	0.894398i	$0.647604\pi$
$104$	3.27075			0.320724
$105$	6.43202	−	5.89834i	0.627701	−	0.575620i
$106$	3.45760	−	3.45760i	0.335832	−	0.335832i
$107$	1.33354	−	1.33354i	0.128919	−	0.128919i	−0.639703	−	0.768622i	$-0.720943\pi$
$107$	1.33354	−	1.33354i	0.128919	−	0.128919i	0.768622	+	0.639703i	$0.220943\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	2.30925	−	2.30925i	0.221186	−	0.221186i	−0.587812	−	0.808998i	$-0.700010\pi$
$109$	2.30925	−	2.30925i	0.221186	−	0.221186i	0.808998	+	0.587812i	$0.200010\pi$
$110$	−0.529665	−	0.577588i	−0.0505015	−	0.0550709i
$111$	0.934944	−	6.01048i	0.0887410	−	0.570490i
$112$	2.75974	−	2.75974i	0.260770	−	0.260770i
$113$	−7.85255			−0.738705			−0.369353	−	0.929289i	$-0.620421\pi$
$113$	−7.85255			−0.738705			−0.369353	+	0.929289i	$0.620421\pi$
$114$	2.84578			0.266532
$115$	−2.05733	+	1.88663i	−0.191847	+	0.175929i
$116$	6.14644	+	6.14644i	0.570683	+	0.570683i
$117$	3.27075			0.302381
$118$	−10.6205	−	10.6205i	−0.977698	−	0.977698i
$119$	−19.5215	+	19.5215i	−1.78953	+	1.78953i
$120$	0.0966903	−	2.23398i	0.00882658	−	0.203933i
$121$	10.8772			0.988834
$122$	1.30384	+	1.30384i	0.118044	+	0.118044i
$123$	−3.94446	−	3.94446i	−0.355660	−	0.355660i
$124$	2.76854	−	2.76854i	0.248622	−	0.248622i
$125$	8.86223	−	6.81623i	0.792662	−	0.609662i
$126$	2.75974	−	2.75974i	0.245857	−	0.245857i
$127$	−14.6420	+	14.6420i	−1.29927	+	1.29927i	−0.370388	+	0.928877i	$0.620775\pi$
$127$	−14.6420	+	14.6420i	−1.29927	+	1.29927i	−0.928877	+	0.370388i	$0.879225\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.28533	−	2.28533i	−0.201212	−	0.201212i
$130$	4.94305	+	5.39030i	0.433534	+	0.472760i
$131$	−3.62929	+	3.62929i	−0.317093	+	0.317093i	−0.847649	−	0.530557i	$-0.821983\pi$
$131$	−3.62929	+	3.62929i	−0.317093	+	0.317093i	0.530557	+	0.847649i	$0.321983\pi$
$132$	−0.247821	−	0.247821i	−0.0215701	−	0.0215701i
$133$			11.1067i			0.963070i
$134$	10.6169	−	10.6169i	0.917164	−	0.917164i
$135$	0.0966903	−	2.23398i	0.00832178	−	0.192270i
$136$			7.07368i			0.606563i
$137$	−12.5315	+	12.5315i	−1.07064	+	1.07064i	−0.0733326	+	0.997308i	$0.523363\pi$
$137$	−12.5315	+	12.5315i	−1.07064	+	1.07064i	−0.997308	+	0.0733326i	$0.976637\pi$
$138$	−0.882722	+	0.882722i	−0.0751423	+	0.0751423i
$139$	−3.66631			−0.310972			−0.155486	−	0.987838i	$-0.549694\pi$
$139$	−3.66631			−0.310972			−0.155486	+	0.987838i	$0.549694\pi$
$140$	8.71889	+	0.377368i	0.736880	+	0.0318934i
$141$			8.14998i			0.686352i
$142$			15.8980i			1.33413i
$143$	1.14631			0.0958590
$144$		−	1.00000i		−	0.0833333i
$145$	−0.840469	+	19.4186i	−0.0697972	+	1.61263i
$146$	−0.998067	−	0.998067i	−0.0826007	−	0.0826007i
$147$	5.82110	+	5.82110i	0.480116	+	0.480116i
$148$	4.91116	−	3.58895i	0.403695	−	0.295010i
$149$		−	16.9433i		−	1.38805i	−0.719951	−	0.694025i	$-0.755836\pi$
$149$		−	16.9433i		−	1.38805i	0.719951	−	0.694025i	$-0.244164\pi$
$150$	3.82779	−	3.21684i	0.312538	−	0.262654i
$151$		−	10.7953i		−	0.878510i	−0.898362	−	0.439255i	$-0.855242\pi$
$151$		−	10.7953i		−	0.878510i	0.898362	−	0.439255i	$-0.144758\pi$
$152$	2.01227	+	2.01227i	0.163217	+	0.163217i
$153$			7.07368i			0.571873i
$154$	0.967210	−	0.967210i	0.0779400	−	0.0779400i
$155$	8.74670	+	0.378572i	0.702552	+	0.0304076i
$156$	2.31277	+	2.31277i	0.185170	+	0.185170i
$157$	6.59408	−	6.59408i	0.526265	−	0.526265i	−0.393192	−	0.919457i	$-0.628629\pi$
$157$	6.59408	−	6.59408i	0.526265	−	0.526265i	0.919457	+	0.393192i	$0.128629\pi$
$158$	−2.47200	−	2.47200i	−0.196662	−	0.196662i
$159$	4.88978			0.387785
$160$	1.64803	−	1.51129i	0.130288	−	0.119478i
$161$	−3.44514	−	3.44514i	−0.271515	−	0.271515i
$162$		−	1.00000i		−	0.0785674i
$163$	−7.00131			−0.548385			−0.274193	−	0.961675i	$-0.588411\pi$
$163$	−7.00131			−0.548385			−0.274193	+	0.961675i	$0.588411\pi$
$164$		−	5.57830i		−	0.435592i
$165$	0.0338872	−	0.782946i	0.00263812	−	0.0609523i
$166$	10.6094	−	10.6094i	0.823451	−	0.823451i
$167$	−14.7018			−1.13766			−0.568830	−	0.822455i	$-0.692604\pi$
$167$	−14.7018			−1.13766			−0.568830	+	0.822455i	$0.692604\pi$
$168$	3.90286			0.301112
$169$	2.30219			0.177091
$170$	−11.6576	+	10.6904i	−0.894101	+	0.819915i
$171$	2.01227	+	2.01227i	0.153882	+	0.153882i
$172$		−	3.23195i		−	0.246434i
$173$	−3.00005	+	3.00005i	−0.228090	+	0.228090i	−0.811894	−	0.583805i	$-0.801563\pi$
$173$	−3.00005	+	3.00005i	−0.228090	+	0.228090i	0.583805	+	0.811894i	$0.301563\pi$
$174$			8.69238i			0.658968i
$175$	12.5548	+	14.9393i	0.949057	+	1.12931i
$176$		−	0.350472i		−	0.0264178i
$177$		−	15.0197i		−	1.12895i
$178$	3.03601	−	3.03601i	0.227559	−	0.227559i
$179$	9.62402	+	9.62402i	0.719333	+	0.719333i	0.968469	−	0.249136i	$-0.0801466\pi$
$179$	9.62402	+	9.62402i	0.719333	+	0.719333i	−0.249136	+	0.968469i	$0.580147\pi$
$180$	1.64803	−	1.51129i	0.122837	−	0.112645i
$181$	14.0878			1.04713			0.523567	−	0.851984i	$-0.324601\pi$
$181$	14.0878			1.04713			0.523567	+	0.851984i	$0.324601\pi$
$182$	−9.02641	+	9.02641i	−0.669082	+	0.669082i
$183$			1.84391i			0.136306i
$184$	−1.24836			−0.0920302
$185$	13.3369	+	2.66980i	0.980546	+	0.196288i
$186$	3.91530			0.287084
$187$			2.47913i			0.181292i
$188$	−5.76291	+	5.76291i	−0.420303	+	0.420303i
$189$	3.90286			0.283891
$190$	−0.275159	+	6.35741i	−0.0199622	+	0.461215i
$191$	2.11691	+	2.11691i	0.153174	+	0.153174i	0.779534	−	0.626360i	$-0.215456\pi$
$191$	2.11691	+	2.11691i	0.153174	+	0.153174i	−0.626360	+	0.779534i	$0.715456\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	20.7874i		−	1.49631i	−0.663525	−	0.748154i	$-0.730940\pi$
$193$		−	20.7874i		−	1.49631i	0.663525	−	0.748154i	$-0.269060\pi$
$194$			7.94277i			0.570257i
$195$	−0.316250	+	7.30678i	−0.0226471	+	0.523249i
$196$			8.23228i			0.588020i
$197$	−11.8547	+	11.8547i	−0.844614	+	0.844614i	−0.989455	−	0.144841i	$-0.953733\pi$
$197$	−11.8547	+	11.8547i	−0.844614	+	0.844614i	0.144841	+	0.989455i	$0.453733\pi$
$198$		−	0.350472i		−	0.0249070i
$199$	6.76638	+	6.76638i	0.479656	+	0.479656i	0.905022	−	0.425366i	$-0.139854\pi$
$199$	6.76638	+	6.76638i	0.479656	+	0.479656i	−0.425366	+	0.905022i	$0.639854\pi$
$200$	4.98130	+	0.432008i	0.352231	+	0.0305476i
$201$	15.0146			1.05905
$202$	−0.514124			−0.0361737
$203$	−33.9251			−2.38108
$204$	−5.00185	+	5.00185i	−0.350200	+	0.350200i
$205$	9.19321	−	8.43043i	0.642082	−	0.588807i
$206$		−	9.07861i		−	0.632537i
$207$	−1.24836			−0.0867669
$208$			3.27075i			0.226786i
$209$	0.705244	+	0.705244i	0.0487828	+	0.0487828i
$210$	5.89834	+	6.43202i	0.407024	+	0.443852i
$211$	−9.92928			−0.683560			−0.341780	−	0.939780i	$-0.611030\pi$
$211$	−9.92928			−0.683560			−0.341780	+	0.939780i	$0.611030\pi$
$212$	3.45760	+	3.45760i	0.237469	+	0.237469i
$213$	−11.2416	+	11.2416i	−0.770261	+	0.770261i
$214$	1.33354	+	1.33354i	0.0911592	+	0.0911592i
$215$	5.32635	−	4.88441i	0.363254	−	0.333114i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$			15.2809i			1.03733i
$218$	2.30925	+	2.30925i	0.156402	+	0.156402i
$219$		−	1.41148i		−	0.0953790i
$220$	0.577588	−	0.529665i	0.0389410	−	0.0357100i
$221$		−	23.1363i		−	1.55631i
$222$	6.01048	+	0.934944i	0.403397	+	0.0627494i
$223$	−6.49659	−	6.49659i	−0.435044	−	0.435044i	0.455296	−	0.890340i	$-0.349533\pi$
$223$	−6.49659	−	6.49659i	−0.435044	−	0.435044i	−0.890340	+	0.455296i	$0.849533\pi$
$224$	2.75974	+	2.75974i	0.184393	+	0.184393i
$225$	4.98130	+	0.432008i	0.332087	+	0.0288005i
$226$		−	7.85255i		−	0.522344i
$227$	−16.6142			−1.10273			−0.551363	−	0.834265i	$-0.685892\pi$
$227$	−16.6142			−1.10273			−0.551363	+	0.834265i	$0.685892\pi$
$228$			2.84578i			0.188466i
$229$		−	2.86631i		−	0.189411i	−0.995505	−	0.0947056i	$-0.969809\pi$
$229$		−	2.86631i		−	0.189411i	0.995505	−	0.0947056i	$-0.0301910\pi$
$230$	−1.88663	−	2.05733i	−0.124401	−	0.135656i
$231$	1.36784			0.0899974
$232$	−6.14644	+	6.14644i	−0.403534	+	0.403534i
$233$	8.37425	−	8.37425i	0.548615	−	0.548615i	−0.377425	−	0.926040i	$-0.623190\pi$
$233$	8.37425	−	8.37425i	0.548615	−	0.548615i	0.926040	+	0.377425i	$0.123190\pi$
$234$			3.27075i			0.213816i
$235$	−18.2069	−	0.788024i	−1.18769	−	0.0514050i
$236$	10.6205	−	10.6205i	0.691337	−	0.691337i
$237$		−	3.49594i		−	0.227085i
$238$	−19.5215	−	19.5215i	−1.26539	−	1.26539i
$239$	16.9584	−	16.9584i	1.09695	−	1.09695i	0.102185	−	0.994765i	$-0.467417\pi$
$239$	16.9584	−	16.9584i	1.09695	−	1.09695i	0.994765	−	0.102185i	$-0.0325834\pi$
$240$	2.23398	+	0.0966903i	0.144203	+	0.00624133i
$241$	9.32818	+	9.32818i	0.600881	+	0.600881i	0.940546	−	0.339665i	$-0.110314\pi$
$241$	9.32818	+	9.32818i	0.600881	+	0.600881i	−0.339665	+	0.940546i	$0.610314\pi$
$242$			10.8772i			0.699211i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−1.30384	+	1.30384i	−0.0834698	+	0.0834698i
$245$	−13.5670	+	12.4414i	−0.866767	+	0.794849i
$246$	3.94446	−	3.94446i	0.251489	−	0.251489i
$247$	−6.58164	−	6.58164i	−0.418780	−	0.418780i
$248$	2.76854	+	2.76854i	0.175802	+	0.175802i
$249$	15.0040			0.950840
$250$	6.81623	+	8.86223i	0.431096	+	0.560496i
$251$	−21.5270	+	21.5270i	−1.35877	+	1.35877i	−0.483333	+	0.875437i	$0.660574\pi$
$251$	−21.5270	+	21.5270i	−1.35877	+	1.35877i	−0.875437	+	0.483333i	$0.839426\pi$
$252$	2.75974	+	2.75974i	0.173847	+	0.173847i
$253$	−0.437515			−0.0275063
$254$	−14.6420	−	14.6420i	−0.918719	−	0.918719i
$255$	−15.8024	−	0.683957i	−0.989587	−	0.0428310i
$256$	1.00000			0.0625000
$257$	−0.409575			−0.0255486			−0.0127743	−	0.999918i	$-0.504066\pi$
$257$	−0.409575			−0.0255486			−0.0127743	+	0.999918i	$0.504066\pi$
$258$	2.28533	−	2.28533i	0.142279	−	0.142279i
$259$	−3.64895	+	23.4580i	−0.226735	+	1.45761i
$260$	−5.39030	+	4.94305i	−0.334292	+	0.306555i
$261$	−6.14644	+	6.14644i	−0.380455	+	0.380455i
$262$	−3.62929	−	3.62929i	−0.224218	−	0.224218i
$263$	10.0366	−	10.0366i	0.618882	−	0.618882i	−0.326362	−	0.945245i	$-0.605823\pi$
$263$	10.0366	−	10.0366i	0.618882	−	0.618882i	0.945245	+	0.326362i	$0.105823\pi$
$264$	0.247821	−	0.247821i	0.0152523	−	0.0152523i
$265$	−0.472795	+	10.9237i	−0.0290435	+	0.671035i
$266$	−11.1067			−0.680994
$267$	4.29357			0.262762
$268$	10.6169	+	10.6169i	0.648533	+	0.648533i
$269$			19.9758i			1.21794i	0.793192	+	0.608972i	$0.208418\pi$
$269$			19.9758i			1.21794i	−0.793192	+	0.608972i	$0.791582\pi$
$270$	2.23398	+	0.0966903i	0.135955	+	0.00588438i
$271$	11.0572			0.671678			0.335839	−	0.941919i	$-0.390980\pi$
$271$	11.0572			0.671678			0.335839	+	0.941919i	$0.390980\pi$
$272$	−7.07368			−0.428905
$273$	−12.7653			−0.772589
$274$	−12.5315	−	12.5315i	−0.757057	−	0.757057i
$275$	1.74581	+	0.151407i	0.105276	+	0.00913016i
$276$	−0.882722	−	0.882722i	−0.0531336	−	0.0531336i
$277$		−	24.4538i		−	1.46929i	−0.678453	−	0.734644i	$-0.737349\pi$
$277$		−	24.4538i		−	1.46929i	0.678453	−	0.734644i	$-0.262651\pi$
$278$		−	3.66631i		−	0.219890i
$279$	2.76854	+	2.76854i	0.165748	+	0.165748i
$280$	−0.377368	+	8.71889i	−0.0225521	+	0.521053i
$281$	−7.23968	−	7.23968i	−0.431883	−	0.431883i	0.457385	−	0.889269i	$-0.348786\pi$
$281$	−7.23968	−	7.23968i	−0.431883	−	0.431883i	−0.889269	+	0.457385i	$0.848786\pi$
$282$	−8.14998			−0.485324
$283$	30.2054			1.79552			0.897761	−	0.440483i	$-0.145193\pi$
$283$	30.2054			1.79552			0.897761	+	0.440483i	$0.145193\pi$
$284$	−15.8980			−0.943373
$285$	−4.68993	+	4.30080i	−0.277808	+	0.254757i
$286$			1.14631i			0.0677825i
$287$	15.3946	+	15.3946i	0.908717	+	0.908717i
$288$	1.00000			0.0589256
$289$	33.0370			1.94335
$290$	−19.4186	−	0.840469i	−1.14030	−	0.0493540i
$291$	−5.61638	+	5.61638i	−0.329238	+	0.329238i
$292$	0.998067	−	0.998067i	0.0584075	−	0.0584075i
$293$	−0.618270	−	0.618270i	−0.0361197	−	0.0361197i	0.688816	−	0.724936i	$-0.258131\pi$
$293$	−0.618270	−	0.618270i	−0.0361197	−	0.0361197i	−0.724936	+	0.688816i	$0.758131\pi$
$294$	−5.82110	+	5.82110i	−0.339494	+	0.339494i
$295$	33.5536	+	1.45226i	1.95357	+	0.0845537i
$296$	3.58895	+	4.91116i	0.208603	+	0.285455i
$297$	0.247821	−	0.247821i	0.0143800	−	0.0143800i
$298$	16.9433			0.981499
$299$	4.08307			0.236130
$300$	3.21684	+	3.82779i	0.185724	+	0.220997i
$301$	8.91933	+	8.91933i	0.514101	+	0.514101i
$302$	10.7953			0.621201
$303$	−0.363541	−	0.363541i	−0.0208849	−	0.0208849i
$304$	−2.01227	+	2.01227i	−0.115412	+	0.115412i
$305$	−4.11925	−	0.178288i	−0.235867	−	0.0102087i
$306$	−7.07368			−0.404376
$307$	8.55841	+	8.55841i	0.488454	+	0.488454i	0.907818	−	0.419364i	$-0.137747\pi$
$307$	8.55841	+	8.55841i	0.488454	+	0.488454i	−0.419364	+	0.907818i	$0.637747\pi$
$308$	0.967210	+	0.967210i	0.0551119	+	0.0551119i
$309$	6.41955	−	6.41955i	0.365195	−	0.365195i
$310$	−0.378572	+	8.74670i	−0.0215014	+	0.496779i
$311$	7.07966	−	7.07966i	0.401451	−	0.401451i	−0.477293	−	0.878744i	$-0.658382\pi$
$311$	7.07966	−	7.07966i	0.401451	−	0.401451i	0.878744	+	0.477293i	$0.158382\pi$
$312$	−2.31277	+	2.31277i	−0.130935	+	0.130935i
$313$		−	21.8518i		−	1.23514i	−0.786518	−	0.617568i	$-0.788118\pi$
$313$		−	21.8518i		−	1.23514i	0.786518	−	0.617568i	$-0.211882\pi$
$314$	6.59408	+	6.59408i	0.372126	+	0.372126i
$315$	−0.377368	+	8.71889i	−0.0212623	+	0.491254i
$316$	2.47200	−	2.47200i	0.139061	−	0.139061i
$317$	19.1074	+	19.1074i	1.07318	+	1.07318i	0.997102	+	0.0760779i	$0.0242398\pi$
$317$	19.1074	+	19.1074i	1.07318	+	1.07318i	0.0760779	+	0.997102i	$0.475760\pi$
$318$			4.88978i			0.274205i
$319$	−2.15416	+	2.15416i	−0.120610	+	0.120610i
$320$	1.51129	+	1.64803i	0.0844837	+	0.0921277i
$321$			1.88592i			0.105262i
$322$	3.44514	−	3.44514i	0.191990	−	0.191990i
$323$	14.2342	−	14.2342i	0.792010	−	0.792010i
$324$	1.00000			0.0555556
$325$	−16.2926	−	1.41299i	−0.903751	−	0.0783786i
$326$		−	7.00131i		−	0.387767i
$327$			3.26578i			0.180598i
$328$	5.57830			0.308010
$329$		−	31.8082i		−	1.75364i
$330$	0.782946	+	0.0338872i	0.0430998	+	0.00186543i
$331$	2.84439	+	2.84439i	0.156342	+	0.156342i	0.780943	−	0.624602i	$-0.214739\pi$
$331$	2.84439	+	2.84439i	0.156342	+	0.156342i	−0.624602	+	0.780943i	$0.714739\pi$
$332$	10.6094	+	10.6094i	0.582268	+	0.582268i
$333$	3.58895	+	4.91116i	0.196673	+	0.269130i
$334$		−	14.7018i		−	0.804447i
$335$	−1.45177	+	33.5423i	−0.0793186	+	1.83261i
$336$			3.90286i			0.212918i
$337$	−12.4436	−	12.4436i	−0.677844	−	0.677844i	0.281668	−	0.959512i	$-0.409112\pi$
$337$	−12.4436	−	12.4436i	−0.677844	−	0.677844i	−0.959512	+	0.281668i	$0.909112\pi$
$338$			2.30219i			0.125222i
$339$	5.55259	−	5.55259i	0.301575	−	0.301575i
$340$	−10.6904	−	11.6576i	−0.579768	−	0.632225i
$341$	0.970295	+	0.970295i	0.0525444	+	0.0525444i
$342$	−2.01227	+	2.01227i	−0.108811	+	0.108811i
$343$	−3.40077	−	3.40077i	−0.183624	−	0.183624i
$344$	3.23195			0.174255
$345$	0.120704	−	2.78880i	0.00649849	−	0.150144i
$346$	−3.00005	−	3.00005i	−0.161284	−	0.161284i
$347$			13.9100i			0.746727i	0.927685	+	0.373363i	$0.121796\pi$
$347$			13.9100i			0.746727i	−0.927685	+	0.373363i	$0.878204\pi$
$348$	−8.69238			−0.465961
$349$		−	0.414422i		−	0.0221835i	−0.999938	−	0.0110918i	$-0.996469\pi$
$349$		−	0.414422i		−	0.0221835i	0.999938	−	0.0110918i	$-0.00353069\pi$
$350$	−14.9393	+	12.5548i	−0.798539	+	0.671085i
$351$	−2.31277	+	2.31277i	−0.123447	+	0.123447i
$352$	0.350472			0.0186802
$353$	29.7855			1.58532			0.792662	−	0.609661i	$-0.208695\pi$
$353$	29.7855			1.58532			0.792662	+	0.609661i	$0.208695\pi$
$354$	15.0197			0.798287
$355$	−24.0265	−	26.2004i	−1.27519	−	1.39057i
$356$	3.03601	+	3.03601i	0.160908	+	0.160908i
$357$		−	27.6076i		−	1.46115i
$358$	−9.62402	+	9.62402i	−0.508645	+	0.508645i
$359$		−	8.57788i		−	0.452723i	−0.974043	−	0.226362i	$-0.927317\pi$
$359$		−	8.57788i		−	0.452723i	0.974043	−	0.226362i	$-0.0726831\pi$
$360$	1.51129	+	1.64803i	0.0796520	+	0.0868588i
$361$			10.9015i			0.573765i
$362$			14.0878i			0.740436i
$363$	−7.69132	+	7.69132i	−0.403690	+	0.403690i
$364$	−9.02641	−	9.02641i	−0.473112	−	0.473112i
$365$	3.15321	+	0.136476i	0.165047	+	0.00714350i
$366$	−1.84391			−0.0963826
$367$	−9.30759	+	9.30759i	−0.485852	+	0.485852i	−0.906995	−	0.421142i	$-0.861629\pi$
$367$	−9.30759	+	9.30759i	−0.485852	+	0.485852i	0.421142	+	0.906995i	$0.361629\pi$
$368$		−	1.24836i		−	0.0650752i
$369$	5.57830			0.290395
$370$	−2.66980	+	13.3369i	−0.138796	+	0.693351i
$371$	−19.0841			−0.990798
$372$			3.91530i			0.202999i
$373$	18.3349	−	18.3349i	0.949345	−	0.949345i	−0.0494321	−	0.998777i	$-0.515741\pi$
$373$	18.3349	−	18.3349i	0.949345	−	0.949345i	0.998777	+	0.0494321i	$0.0157411\pi$
$374$	−2.47913			−0.128193
$375$	−1.44674	+	11.0863i	−0.0747093	+	0.572496i
$376$	−5.76291	−	5.76291i	−0.297199	−	0.297199i
$377$	20.1035	−	20.1035i	1.03538	−	1.03538i
$378$			3.90286i			0.200741i
$379$			0.736373i			0.0378249i	0.999821	+	0.0189125i	$0.00602038\pi$
$379$			0.736373i			0.0378249i	−0.999821	+	0.0189125i	$0.993980\pi$
$380$	−6.35741	−	0.275159i	−0.326128	−	0.0141154i
$381$		−	20.7069i		−	1.06085i
$382$	−2.11691	+	2.11691i	−0.108311	+	0.108311i
$383$			2.85854i			0.146065i	0.997330	+	0.0730323i	$0.0232676\pi$
$383$			2.85854i			0.146065i	−0.997330	+	0.0730323i	$0.976732\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−0.132257	+	3.05573i	−0.00674044	+	0.155734i
$386$	20.7874			1.05805
$387$	3.23195			0.164289
$388$	−7.94277			−0.403233
$389$	−14.3095	+	14.3095i	−0.725519	+	0.725519i	−0.969724	−	0.244205i	$-0.921473\pi$
$389$	−14.3095	+	14.3095i	−0.725519	+	0.725519i	0.244205	+	0.969724i	$0.421473\pi$
$390$	−7.30678	−	0.316250i	−0.369993	−	0.0160139i
$391$			8.83049i			0.446577i
$392$	−8.23228			−0.415793
$393$		−	5.13259i		−	0.258905i
$394$	−11.8547	−	11.8547i	−0.597233	−	0.597233i
$395$	7.80984	+	0.338023i	0.392956	+	0.0170078i
$396$	0.350472			0.0176119
$397$	0.498839	+	0.498839i	0.0250360	+	0.0250360i	0.719514	−	0.694478i	$-0.244365\pi$
$397$	0.498839	+	0.498839i	0.0250360	+	0.0250360i	−0.694478	+	0.719514i	$0.744365\pi$
$398$	−6.76638	+	6.76638i	−0.339168	+	0.339168i
$399$	−7.85360	−	7.85360i	−0.393172	−	0.393172i
$400$	−0.432008	+	4.98130i	−0.0216004	+	0.249065i
$401$	10.8582	−	10.8582i	0.542234	−	0.542234i	−0.381949	−	0.924183i	$-0.624747\pi$
$401$	10.8582	−	10.8582i	0.542234	−	0.542234i	0.924183	+	0.381949i	$0.124747\pi$
$402$			15.0146i			0.748861i
$403$	−9.05520	−	9.05520i	−0.451072	−	0.451072i
$404$		−	0.514124i		−	0.0255786i
$405$	1.51129	+	1.64803i	0.0750966	+	0.0818913i
$406$		−	33.9251i		−	1.68368i
$407$	1.25783	+	1.72122i	0.0623481	+	0.0853179i
$408$	−5.00185	−	5.00185i	−0.247628	−	0.247628i
$409$	−7.92408	−	7.92408i	−0.391820	−	0.391820i	0.483515	−	0.875336i	$-0.339360\pi$
$409$	−7.92408	−	7.92408i	−0.391820	−	0.391820i	−0.875336	+	0.483515i	$0.839360\pi$
$410$	8.43043	+	9.19321i	0.416349	+	0.454020i
$411$		−	17.7222i		−	0.874174i
$412$	9.07861			0.447271
$413$			58.6196i			2.88448i
$414$		−	1.24836i		−	0.0613535i
$415$	−1.45074	+	33.5186i	−0.0712141	+	1.64536i
$416$	−3.27075			−0.160362
$417$	2.59247	−	2.59247i	0.126954	−	0.126954i
$418$	−0.705244	+	0.705244i	−0.0344946	+	0.0344946i
$419$			13.1368i			0.641775i	0.947117	+	0.320887i	$0.103981\pi$
$419$			13.1368i			0.641775i	−0.947117	+	0.320887i	$0.896019\pi$
$420$	−6.43202	+	5.89834i	−0.313851	+	0.287810i
$421$	10.6585	−	10.6585i	0.519461	−	0.519461i	−0.397947	−	0.917408i	$-0.630277\pi$
$421$	10.6585	−	10.6585i	0.519461	−	0.519461i	0.917408	+	0.397947i	$0.130277\pi$
$422$		−	9.92928i		−	0.483350i
$423$	−5.76291	−	5.76291i	−0.280202	−	0.280202i
$424$	−3.45760	+	3.45760i	−0.167916	+	0.167916i
$425$	3.05589	−	35.2362i	0.148232	−	1.70920i
$426$	−11.2416	−	11.2416i	−0.544657	−	0.544657i
$427$		−	7.19651i		−	0.348263i
$428$	−1.33354	+	1.33354i	−0.0644593	+	0.0644593i
$429$	−0.810561	+	0.810561i	−0.0391343	+	0.0391343i
$430$	4.88441	+	5.32635i	0.235547	+	0.256859i
$431$	−13.6585	+	13.6585i	−0.657907	+	0.657907i	−0.954884	−	0.296978i	$-0.904021\pi$
$431$	−13.6585	+	13.6585i	−0.657907	+	0.657907i	0.296978	+	0.954884i	$0.404021\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−16.2196	−	16.2196i	−0.779466	−	0.779466i	0.200274	−	0.979740i	$-0.435817\pi$
$433$	−16.2196	−	16.2196i	−0.779466	−	0.779466i	−0.979740	+	0.200274i	$0.935817\pi$
$434$	−15.2809			−0.733505
$435$	−13.1367	−	14.3253i	−0.629857	−	0.686846i
$436$	−2.30925	+	2.30925i	−0.110593	+	0.110593i
$437$	2.51203	+	2.51203i	0.120167	+	0.120167i
$438$	1.41148			0.0674431
$439$	4.52525	+	4.52525i	0.215979	+	0.215979i	0.806801	−	0.590823i	$-0.201197\pi$
$439$	4.52525	+	4.52525i	0.215979	+	0.215979i	−0.590823	+	0.806801i	$0.701197\pi$
$440$	0.529665	+	0.577588i	0.0252508	+	0.0275354i
$441$	−8.23228			−0.392013
$442$	23.1363			1.10048
$443$	−17.5292	+	17.5292i	−0.832839	+	0.832839i	−0.987904	−	0.155066i	$-0.950441\pi$
$443$	−17.5292	+	17.5292i	−0.832839	+	0.832839i	0.155066	+	0.987904i	$0.450441\pi$
$444$	−0.934944	+	6.01048i	−0.0443705	+	0.285245i
$445$	−0.415146	+	9.59172i	−0.0196798	+	0.454691i
$446$	6.49659	−	6.49659i	0.307623	−	0.307623i
$447$	11.9807	+	11.9807i	0.566669	+	0.566669i
$448$	−2.75974	+	2.75974i	−0.130385	+	0.130385i
$449$	24.1689	−	24.1689i	1.14060	−	1.14060i	0.152263	−	0.988340i	$-0.451344\pi$
$449$	24.1689	−	24.1689i	1.14060	−	1.14060i	0.988340	−	0.152263i	$-0.0486561\pi$
$450$	−0.432008	+	4.98130i	−0.0203650	+	0.234821i
$451$	1.95504			0.0920592
$452$	7.85255			0.369353
$453$	7.63344	+	7.63344i	0.358650	+	0.358650i
$454$		−	16.6142i		−	0.779745i
$455$	1.23428	−	28.5173i	0.0578638	−	1.33691i
$456$	−2.84578			−0.133266
$457$	−15.3091			−0.716131			−0.358065	−	0.933697i	$-0.616564\pi$
$457$	−15.3091			−0.716131			−0.358065	+	0.933697i	$0.616564\pi$
$458$	2.86631			0.133934
$459$	−5.00185	−	5.00185i	−0.233466	−	0.233466i
$460$	2.05733	−	1.88663i	0.0959236	−	0.0879646i
$461$	19.6061	+	19.6061i	0.913145	+	0.913145i	0.996518	−	0.0833730i	$-0.0265693\pi$
$461$	19.6061	+	19.6061i	0.913145	+	0.913145i	−0.0833730	+	0.996518i	$0.526569\pi$
$462$			1.36784i			0.0636377i
$463$		−	25.4617i		−	1.18331i	−0.806192	−	0.591653i	$-0.798475\pi$
$463$		−	25.4617i		−	1.18331i	0.806192	−	0.591653i	$-0.201525\pi$
$464$	−6.14644	−	6.14644i	−0.285341	−	0.285341i
$465$	−6.45254	+	5.91716i	−0.299229	+	0.274402i
$466$	8.37425	+	8.37425i	0.387930	+	0.387930i
$467$	18.9252			0.875752			0.437876	−	0.899035i	$-0.355731\pi$
$467$	18.9252			0.875752			0.437876	+	0.899035i	$0.355731\pi$
$468$	−3.27075			−0.151191
$469$	−58.5999			−2.70589
$470$	0.788024	−	18.2069i	0.0363488	−	0.839820i
$471$			9.32544i			0.429694i
$472$	10.6205	+	10.6205i	0.488849	+	0.488849i
$473$	1.13271			0.0520820
$474$	3.49594			0.160574
$475$	−9.15441	−	10.8930i	−0.420033	−	0.499807i
$476$	19.5215	−	19.5215i	0.894766	−	0.894766i
$477$	−3.45760	+	3.45760i	−0.158313	+	0.158313i
$478$	16.9584	+	16.9584i	0.775661	+	0.775661i
$479$	3.00653	−	3.00653i	0.137372	−	0.137372i	−0.635077	−	0.772449i	$-0.719032\pi$
$479$	3.00653	−	3.00653i	0.137372	−	0.137372i	0.772449	+	0.635077i	$0.219032\pi$
$480$	−0.0966903	+	2.23398i	−0.00441329	+	0.101967i
$481$	−11.7386	−	16.0632i	−0.535232	−	0.732418i
$482$	−9.32818	+	9.32818i	−0.424887	+	0.424887i
$483$	4.87216			0.221691
$484$	−10.8772			−0.494417
$485$	−12.0038	−	13.0899i	−0.545065	−	0.594383i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	−42.0200			−1.90411			−0.952054	−	0.305929i	$-0.901033\pi$
$487$	−42.0200			−1.90411			−0.952054	+	0.305929i	$0.901033\pi$
$488$	−1.30384	−	1.30384i	−0.0590221	−	0.0590221i
$489$	4.95068	−	4.95068i	0.223877	−	0.223877i
$490$	−12.4414	−	13.5670i	−0.562043	−	0.612897i
$491$	14.2813			0.644507			0.322254	−	0.946653i	$-0.395560\pi$
$491$	14.2813			0.644507			0.322254	+	0.946653i	$0.395560\pi$
$492$	3.94446	+	3.94446i	0.177830	+	0.177830i
$493$	43.4780	+	43.4780i	1.95815	+	1.95815i
$494$	6.58164	−	6.58164i	0.296122	−	0.296122i
$495$	0.529665	+	0.577588i	0.0238067	+	0.0259607i
$496$	−2.76854	+	2.76854i	−0.124311	+	0.124311i
$497$	43.8743	−	43.8743i	1.96803	−	1.96803i
$498$			15.0040i			0.672345i
$499$	−4.58214	−	4.58214i	−0.205125	−	0.205125i	0.597067	−	0.802192i	$-0.296333\pi$
$499$	−4.58214	−	4.58214i	−0.205125	−	0.205125i	−0.802192	+	0.597067i	$0.796333\pi$
$500$	−8.86223	+	6.81623i	−0.396331	+	0.304831i
$501$	10.3957	−	10.3957i	0.464447	−	0.464447i
$502$	−21.5270	−	21.5270i	−0.960795	−	0.960795i
$503$			4.41445i			0.196831i	0.995145	+	0.0984153i	$0.0313774\pi$
$503$			4.41445i			0.196831i	−0.995145	+	0.0984153i	$0.968623\pi$
$504$	−2.75974	+	2.75974i	−0.122928	+	0.122928i
$505$	0.847293	−	0.776991i	0.0377040	−	0.0345756i
$506$		−	0.437515i		−	0.0194499i
$507$	−1.62789	+	1.62789i	−0.0722972	+	0.0722972i
$508$	14.6420	−	14.6420i	0.649633	−	0.649633i
$509$	−23.7000			−1.05048			−0.525242	−	0.850953i	$-0.676025\pi$
$509$	−23.7000			−1.05048			−0.525242	+	0.850953i	$0.676025\pi$
$510$	0.683957	−	15.8024i	0.0302861	−	0.699744i
$511$			5.50880i			0.243695i
$512$			1.00000i			0.0441942i
$513$	−2.84578			−0.125644
$514$		−	0.409575i		−	0.0180656i
$515$	13.7204	+	14.9618i	0.604594	+	0.659297i
$516$	2.28533	+	2.28533i	0.100606	+	0.100606i
$517$	−2.01974	−	2.01974i	−0.0888279	−	0.0888279i
$518$	−23.4580	−	3.64895i	−1.03069	−	0.160326i
$519$		−	4.24271i		−	0.186234i
$520$	−4.94305	−	5.39030i	−0.216767	−	0.236380i
$521$		−	22.6223i		−	0.991100i	−0.868579	−	0.495550i	$-0.834966\pi$
$521$		−	22.6223i		−	0.991100i	0.868579	−	0.495550i	$-0.165034\pi$
$522$	−6.14644	−	6.14644i	−0.269023	−	0.269023i
$523$		−	38.2884i		−	1.67424i	−0.547023	−	0.837118i	$-0.684239\pi$
$523$		−	38.2884i		−	1.67424i	0.547023	−	0.837118i	$-0.315761\pi$
$524$	3.62929	−	3.62929i	0.158546	−	0.158546i
$525$	−19.4413	−	1.68606i	−0.848488	−	0.0735858i
$526$	10.0366	+	10.0366i	0.437616	+	0.437616i
$527$	19.5838	−	19.5838i	0.853082	−	0.853082i
$528$	0.247821	+	0.247821i	0.0107850	+	0.0107850i
$529$	21.4416			0.932244
$530$	−10.9237	−	0.472795i	−0.474494	−	0.0205369i
$531$	10.6205	+	10.6205i	0.460891	+	0.460891i
$532$		−	11.1067i		−	0.481535i
$533$	−18.2452			−0.790289
$534$			4.29357i			0.185801i
$535$	−4.21309	−	0.182350i	−0.182148	−	0.00788367i
$536$	−10.6169	+	10.6169i	−0.458582	+	0.458582i
$537$	−13.6104			−0.587333
$538$	−19.9758			−0.861217
$539$	−2.88518			−0.124274
$540$	−0.0966903	+	2.23398i	−0.00416089	+	0.0961350i
$541$	8.89780	+	8.89780i	0.382546	+	0.382546i	0.872019	−	0.489472i	$-0.162811\pi$
$541$	8.89780	+	8.89780i	0.382546	+	0.382546i	−0.489472	+	0.872019i	$0.662811\pi$
$542$			11.0572i			0.474948i
$543$	−9.96155	+	9.96155i	−0.427491	+	0.427491i
$544$		−	7.07368i		−	0.303282i
$545$	−7.29567	−	0.315769i	−0.312512	−	0.0135260i
$546$		−	12.7653i		−	0.546303i
$547$		−	7.12339i		−	0.304574i	−0.988336	−	0.152287i	$-0.951336\pi$
$547$		−	7.12339i		−	0.304574i	0.988336	−	0.152287i	$-0.0486638\pi$
$548$	12.5315	−	12.5315i	0.535320	−	0.535320i
$549$	−1.30384	−	1.30384i	−0.0556465	−	0.0556465i
$550$	−0.151407	+	1.74581i	−0.00645600	+	0.0744414i
$551$	24.7366			1.05382
$552$	0.882722	−	0.882722i	0.0375712	−	0.0375712i
$553$			13.6441i			0.580208i
$554$	24.4538			1.03894
$555$	−11.3184	+	7.54276i	−0.480440	+	0.320172i
$556$	3.66631			0.155486
$557$		−	45.3868i		−	1.92310i	−0.274626	−	0.961551i	$-0.588554\pi$
$557$		−	45.3868i		−	1.92310i	0.274626	−	0.961551i	$-0.411446\pi$
$558$	−2.76854	+	2.76854i	−0.117202	+	0.117202i
$559$	−10.5709			−0.447102
$560$	−8.71889	−	0.377368i	−0.368440	−	0.0159467i
$561$	−1.75301	−	1.75301i	−0.0740121	−	0.0740121i
$562$	7.23968	−	7.23968i	0.305388	−	0.305388i
$563$			5.35148i			0.225538i	0.993621	+	0.112769i	$0.0359720\pi$
$563$			5.35148i			0.225538i	−0.993621	+	0.112769i	$0.964028\pi$
$564$		−	8.14998i		−	0.343176i
$565$	11.8675	+	12.9412i	0.499268	+	0.544442i
$566$			30.2054i			1.26963i
$567$	−2.75974	+	2.75974i	−0.115898	+	0.115898i
$568$		−	15.8980i		−	0.667066i
$569$	13.2588	+	13.2588i	0.555837	+	0.555837i	0.928119	−	0.372283i	$-0.121425\pi$
$569$	13.2588	+	13.2588i	0.555837	+	0.555837i	−0.372283	+	0.928119i	$0.621425\pi$
$570$	−4.30080	−	4.68993i	−0.180141	−	0.196440i
$571$	−39.9897			−1.67352			−0.836758	−	0.547574i	$-0.815552\pi$
$571$	−39.9897			−1.67352			−0.836758	+	0.547574i	$0.815552\pi$
$572$	−1.14631			−0.0479295
$573$	−2.99376			−0.125066
$574$	−15.3946	+	15.3946i	−0.642560	+	0.642560i
$575$	6.21845	+	0.539300i	0.259327	+	0.0224904i
$576$			1.00000i			0.0416667i
$577$	2.19671			0.0914503			0.0457251	−	0.998954i	$-0.485440\pi$
$577$	2.19671			0.0914503			0.0457251	+	0.998954i	$0.485440\pi$
$578$			33.0370i			1.37416i
$579$	14.6989	+	14.6989i	0.610865	+	0.610865i
$580$	0.840469	−	19.4186i	0.0348986	−	0.806313i
$581$	−58.5584			−2.42941
$582$	−5.61638	−	5.61638i	−0.232807	−	0.232807i
$583$	−1.21179	+	1.21179i	−0.0501873	+	0.0501873i
$584$	0.998067	+	0.998067i	0.0413003	+	0.0413003i
$585$	−4.94305	−	5.39030i	−0.204370	−	0.222861i
$586$	0.618270	−	0.618270i	0.0255405	−	0.0255405i
$587$		−	40.3393i		−	1.66498i	−0.554041	−	0.832490i	$-0.686915\pi$
$587$		−	40.3393i		−	1.66498i	0.554041	−	0.832490i	$-0.313085\pi$
$588$	−5.82110	−	5.82110i	−0.240058	−	0.240058i
$589$		−	11.1421i		−	0.459102i
$590$	−1.45226	+	33.5536i	−0.0597885	+	1.38138i
$591$		−	16.7651i		−	0.689625i
$592$	−4.91116	+	3.58895i	−0.201847	+	0.147505i
$593$	−14.1348	−	14.1348i	−0.580448	−	0.580448i	0.354579	−	0.935026i	$-0.384624\pi$
$593$	−14.1348	−	14.1348i	−0.580448	−	0.580448i	−0.935026	+	0.354579i	$0.884624\pi$
$594$	0.247821	+	0.247821i	0.0101682	+	0.0101682i
$595$	61.6747	+	2.66938i	2.52841	+	0.109434i
$596$			16.9433i			0.694025i
$597$	−9.56911			−0.391638
$598$			4.08307i			0.166969i
$599$		−	23.9120i		−	0.977016i	−0.872559	−	0.488508i	$-0.837541\pi$
$599$		−	23.9120i		−	0.977016i	0.872559	−	0.488508i	$-0.162459\pi$
$600$	−3.82779	+	3.21684i	−0.156269	+	0.131327i
$601$	−24.5648			−1.00202			−0.501009	−	0.865442i	$-0.667038\pi$
$601$	−24.5648			−1.00202			−0.501009	+	0.865442i	$0.667038\pi$
$602$	−8.91933	+	8.91933i	−0.363525	+	0.363525i
$603$	−10.6169	+	10.6169i	−0.432355	+	0.432355i
$604$			10.7953i			0.439255i
$605$	−16.4386	−	17.9259i	−0.668322	−	0.728792i
$606$	0.363541	−	0.363541i	0.0147678	−	0.0147678i
$607$			28.5020i			1.15686i	0.815732	+	0.578430i	$0.196334\pi$
$607$			28.5020i			1.15686i	−0.815732	+	0.578430i	$0.803666\pi$
$608$	−2.01227	−	2.01227i	−0.0816084	−	0.0816084i
$609$	23.9887	−	23.9887i	0.972070	−	0.972070i
$610$	0.178288	−	4.11925i	0.00721867	−	0.166783i
$611$	18.8490	+	18.8490i	0.762550	+	0.762550i
$612$		−	7.07368i		−	0.285937i
$613$	−20.5098	+	20.5098i	−0.828384	+	0.828384i	−0.987293	−	0.158909i	$-0.949202\pi$
$613$	−20.5098	+	20.5098i	−0.828384	+	0.828384i	0.158909	+	0.987293i	$0.449202\pi$
$614$	−8.55841	+	8.55841i	−0.345389	+	0.345389i
$615$	−0.539368	+	12.4618i	−0.0217494	+	0.502508i
$616$	−0.967210	+	0.967210i	−0.0389700	+	0.0389700i
$617$	−14.5571	−	14.5571i	−0.586047	−	0.586047i	0.350511	−	0.936559i	$-0.386008\pi$
$617$	−14.5571	−	14.5571i	−0.586047	−	0.586047i	−0.936559	+	0.350511i	$0.886008\pi$
$618$	6.41955	+	6.41955i	0.258232	+	0.258232i
$619$	−22.6423			−0.910070			−0.455035	−	0.890474i	$-0.650373\pi$
$619$	−22.6423			−0.910070			−0.455035	+	0.890474i	$0.650373\pi$
$620$	−8.74670	−	0.378572i	−0.351276	−	0.0152038i
$621$	0.882722	−	0.882722i	0.0354224	−	0.0354224i
$622$	7.07966	+	7.07966i	0.283869	+	0.283869i
$623$	−16.7572			−0.671362
$624$	−2.31277	−	2.31277i	−0.0925849	−	0.0925849i
$625$	−24.6267	−	4.30392i	−0.985070	−	0.172157i
$626$	21.8518			0.873372
$627$	−0.997366			−0.0398310
$628$	−6.59408	+	6.59408i	−0.263132	+	0.263132i
$629$	34.7400	−	25.3871i	1.38517	−	1.01225i
$630$	−8.71889	−	0.377368i	−0.347369	−	0.0150347i
$631$	23.0961	−	23.0961i	0.919443	−	0.919443i	−0.0775462	−	0.996989i	$-0.524709\pi$
$631$	23.0961	−	23.0961i	0.919443	−	0.919443i	0.996989	+	0.0775462i	$0.0247085\pi$
$632$	2.47200	+	2.47200i	0.0983309	+	0.0983309i
$633$	7.02106	−	7.02106i	0.279062	−	0.279062i
$634$	−19.1074	+	19.1074i	−0.758853	+	0.758853i
$635$	46.2587	+	2.00215i	1.83572	+	0.0794531i
$636$	−4.88978			−0.193893
$637$	26.9257			1.06684
$638$	−2.15416	−	2.15416i	−0.0852839	−	0.0852839i
$639$		−	15.8980i		−	0.628916i
$640$	−1.64803	+	1.51129i	−0.0651441	+	0.0597390i
$641$	−42.5772			−1.68170			−0.840849	−	0.541269i	$-0.817944\pi$
$641$	−42.5772			−1.68170			−0.840849	+	0.541269i	$0.817944\pi$
$642$	−1.88592			−0.0744312
$643$	19.1904			0.756794			0.378397	−	0.925643i	$-0.376475\pi$
$643$	19.1904			0.756794			0.378397	+	0.925643i	$0.376475\pi$
$644$	3.44514	+	3.44514i	0.135757	+	0.135757i
$645$	−0.312498	+	7.22010i	−0.0123046	+	0.284291i
$646$	14.2342	+	14.2342i	0.560036	+	0.560036i
$647$			28.2302i			1.10984i	0.831903	+	0.554921i	$0.187251\pi$
$647$			28.2302i			1.10984i	−0.831903	+	0.554921i	$0.812749\pi$
$648$			1.00000i			0.0392837i
$649$	3.72219	+	3.72219i	0.146109	+	0.146109i
$650$	1.41299	−	16.2926i	0.0554220	−	0.639048i
$651$	−10.8052	−	10.8052i	−0.423489	−	0.423489i
$652$	7.00131			0.274193
$653$	5.24225			0.205145			0.102573	−	0.994726i	$-0.467293\pi$
$653$	5.24225			0.205145			0.102573	+	0.994726i	$0.467293\pi$
$654$	−3.26578			−0.127702
$655$	11.4661	+	0.496272i	0.448017	+	0.0193910i
$656$			5.57830i			0.217796i
$657$	0.998067	+	0.998067i	0.0389383	+	0.0389383i
$658$	31.8082			1.24001
$659$	−30.0925			−1.17224			−0.586119	−	0.810225i	$-0.699345\pi$
$659$	−30.0925			−1.17224			−0.586119	+	0.810225i	$0.699345\pi$
$660$	−0.0338872	+	0.782946i	−0.00131906	+	0.0304761i
$661$	−32.5054	+	32.5054i	−1.26432	+	1.26432i	−0.315335	+	0.948981i	$0.602117\pi$
$661$	−32.5054	+	32.5054i	−1.26432	+	1.26432i	−0.948981	+	0.315335i	$0.897883\pi$
$662$	−2.84439	+	2.84439i	−0.110550	+	0.110550i
$663$	16.3598	+	16.3598i	0.635362	+	0.635362i
$664$	−10.6094	+	10.6094i	−0.411726	+	0.411726i
$665$	18.3041	−	16.7854i	0.709804	−	0.650910i
$666$	−4.91116	+	3.58895i	−0.190303	+	0.139069i
$667$	−7.67296	+	7.67296i	−0.297098	+	0.297098i
$668$	14.7018			0.568830
$669$	9.18757			0.355212
$670$	−33.5423	−	1.45177i	−1.29585	−	0.0560867i
$671$	−0.456959	−	0.456959i	−0.0176407	−	0.0176407i
$672$	−3.90286			−0.150556
$673$	−9.11977	−	9.11977i	−0.351541	−	0.351541i	0.509141	−	0.860683i	$-0.329963\pi$
$673$	−9.11977	−	9.11977i	−0.351541	−	0.351541i	−0.860683	+	0.509141i	$0.829963\pi$
$674$	12.4436	−	12.4436i	0.479308	−	0.479308i
$675$	−3.82779	+	3.21684i	−0.147332	+	0.123816i
$676$	−2.30219			−0.0885456
$677$	19.8062	+	19.8062i	0.761213	+	0.761213i	0.976542	−	0.215329i	$-0.0690823\pi$
$677$	19.8062	+	19.8062i	0.761213	+	0.761213i	−0.215329	+	0.976542i	$0.569082\pi$
$678$	5.55259	+	5.55259i	0.213246	+	0.213246i
$679$	21.9199	−	21.9199i	0.841210	−	0.841210i
$680$	11.6576	−	10.6904i	0.447050	−	0.409958i
$681$	11.7480	−	11.7480i	0.450186	−	0.450186i
$682$	−0.970295	+	0.970295i	−0.0371545	+	0.0371545i
$683$		−	9.00362i		−	0.344514i	−0.985052	−	0.172257i	$-0.944894\pi$
$683$		−	9.00362i		−	0.344514i	0.985052	−	0.172257i	$-0.0551060\pi$
$684$	−2.01227	−	2.01227i	−0.0769411	−	0.0769411i
$685$	39.5911	+	1.71357i	1.51270	+	0.0654721i
$686$	3.40077	−	3.40077i	0.129842	−	0.129842i
$687$	2.02679	+	2.02679i	0.0773268	+	0.0773268i
$688$			3.23195i			0.123217i
$689$	11.3089	−	11.3089i	0.430837	−	0.430837i
$690$	2.78880	+	0.120704i	0.106168	+	0.00459513i
$691$			8.79710i			0.334657i	0.985901	+	0.167329i	$0.0535141\pi$
$691$			8.79710i			0.334657i	−0.985901	+	0.167329i	$0.946486\pi$
$692$	3.00005	−	3.00005i	0.114045	−	0.114045i
$693$	−0.967210	+	0.967210i	−0.0367413	+	0.0367413i
$694$	−13.9100			−0.528016
$695$	5.54085	+	6.04219i	0.210176	+	0.229193i
$696$		−	8.69238i		−	0.329484i
$697$		−	39.4592i		−	1.49462i
$698$	0.414422			0.0156861
$699$			11.8430i			0.447943i
$700$	−12.5548	−	14.9393i	−0.474529	−	0.564653i
$701$	6.74494	+	6.74494i	0.254753	+	0.254753i	0.822916	−	0.568163i	$-0.192346\pi$
$701$	6.74494	+	6.74494i	0.254753	+	0.254753i	−0.568163	+	0.822916i	$0.692346\pi$
$702$	−2.31277	−	2.31277i	−0.0872899	−	0.0872899i
$703$	2.66065	−	17.1045i	0.100348	−	0.645109i
$704$			0.350472i			0.0132089i
$705$	13.4314	−	12.3170i	0.505856	−	0.463884i
$706$			29.7855i			1.12099i
$707$	1.41885	+	1.41885i	0.0533612	+	0.0533612i
$708$			15.0197i			0.564474i
$709$	−27.6225	+	27.6225i	−1.03739	+	1.03739i	−0.0381132	+	0.999273i	$0.512135\pi$
$709$	−27.6225	+	27.6225i	−1.03739	+	1.03739i	−0.999273	+	0.0381132i	$0.987865\pi$
$710$	26.2004	−	24.0265i	0.983284	−	0.901698i
$711$	2.47200	+	2.47200i	0.0927072	+	0.0927072i
$712$	−3.03601	+	3.03601i	−0.113779	+	0.113779i
$713$	3.45613	+	3.45613i	0.129433	+	0.129433i
$714$	27.6076			1.03319
$715$	−1.73240	−	1.88915i	−0.0647881	−	0.0706501i
$716$	−9.62402	−	9.62402i	−0.359666	−	0.359666i
$717$			23.9829i			0.895656i
$718$	8.57788			0.320124
$719$			11.0173i			0.410878i	0.978670	+	0.205439i	$0.0658622\pi$
$719$			11.0173i			0.410878i	−0.978670	+	0.205439i	$0.934138\pi$
$720$	−1.64803	+	1.51129i	−0.0614185	+	0.0563224i
$721$	−25.0546	+	25.0546i	−0.933081	+	0.933081i
$722$	−10.9015			−0.405713
$723$	−13.1920			−0.490617
$724$	−14.0878			−0.523567
$725$	33.2726	−	27.9620i	1.23571	−	1.03848i
$726$	−7.69132	−	7.69132i	−0.285452	−	0.285452i
$727$		−	8.80697i		−	0.326632i	−0.986574	−	0.163316i	$-0.947781\pi$
$727$		−	8.80697i		−	0.326632i	0.986574	−	0.163316i	$-0.0522191\pi$
$728$	9.02641	−	9.02641i	0.334541	−	0.334541i
$729$			1.00000i			0.0370370i
$730$	−0.136476	+	3.15321i	−0.00505122	+	0.116706i
$731$		−	22.8618i		−	0.845574i
$732$		−	1.84391i		−	0.0681528i
$733$	−11.9215	+	11.9215i	−0.440331	+	0.440331i	−0.892123	−	0.451792i	$-0.850785\pi$
$733$	−11.9215	+	11.9215i	−0.440331	+	0.440331i	0.451792	+	0.892123i	$0.350785\pi$
$734$	−9.30759	−	9.30759i	−0.343549	−	0.343549i
$735$	0.795982	−	18.3907i	0.0293602	−	0.678352i
$736$	1.24836			0.0460151
$737$	−3.72094	+	3.72094i	−0.137063	+	0.137063i
$738$			5.57830i			0.205340i
$739$	1.03649			0.0381277			0.0190639	−	0.999818i	$-0.493931\pi$
$739$	1.03649			0.0381277			0.0190639	+	0.999818i	$0.493931\pi$
$740$	−13.3369	−	2.66980i	−0.490273	−	0.0981438i
$741$	9.30784			0.341932
$742$		−	19.0841i		−	0.700600i
$743$	−16.2854	+	16.2854i	−0.597453	+	0.597453i	−0.939634	−	0.342181i	$-0.888834\pi$
$743$	−16.2854	+	16.2854i	−0.597453	+	0.597453i	0.342181	+	0.939634i	$0.388834\pi$
$744$	−3.91530			−0.143542
$745$	−27.9231	+	25.6062i	−1.02302	+	0.938140i
$746$	18.3349	+	18.3349i	0.671289	+	0.671289i
$747$	−10.6094	+	10.6094i	−0.388179	+	0.388179i
$748$		−	2.47913i		−	0.0906459i
$749$		−	7.36046i		−	0.268945i
$750$	−11.0863	−	1.44674i	−0.404816	−	0.0528274i
$751$		−	44.5447i		−	1.62546i	−0.582641	−	0.812729i	$-0.697981\pi$
$751$		−	44.5447i		−	1.62546i	0.582641	−	0.812729i	$-0.302019\pi$
$752$	5.76291	−	5.76291i	0.210152	−	0.210152i
$753$		−	30.4437i		−	1.10943i
$754$	20.1035	+	20.1035i	0.732126	+	0.732126i
$755$	−17.7910	+	16.3148i	−0.647481	+	0.593758i
$756$	−3.90286			−0.141945
$757$	−6.50328			−0.236366			−0.118183	−	0.992992i	$-0.537707\pi$
$757$	−6.50328			−0.236366			−0.118183	+	0.992992i	$0.537707\pi$
$758$	−0.736373			−0.0267463
$759$	0.309369	−	0.309369i	0.0112294	−	0.0112294i
$760$	0.275159	−	6.35741i	0.00998108	−	0.230607i
$761$		−	30.3235i		−	1.09923i	−0.835419	−	0.549613i	$-0.814775\pi$
$761$		−	30.3235i		−	1.09923i	0.835419	−	0.549613i	$-0.185225\pi$
$762$	20.7069			0.750131
$763$		−	12.7459i		−	0.461431i
$764$	−2.11691	−	2.11691i	−0.0765871	−	0.0765871i
$765$	11.6576	−	10.6904i	0.421483	−	0.386512i
$766$	−2.85854			−0.103283
$767$	−34.7371	−	34.7371i	−1.25428	−	1.25428i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	20.4408	+	20.4408i	0.737113	+	0.737113i	0.972018	−	0.234906i	$-0.0754781\pi$
$769$	20.4408	+	20.4408i	0.737113	+	0.737113i	−0.234906	+	0.972018i	$0.575478\pi$
$770$	−3.05573	−	0.132257i	−0.110121	−	0.00476621i
$771$	0.289614	−	0.289614i	0.0104302	−	0.0104302i
$772$			20.7874i			0.748154i
$773$	−12.8496	−	12.8496i	−0.462167	−	0.462167i	0.437198	−	0.899365i	$-0.355971\pi$
$773$	−12.8496	−	12.8496i	−0.462167	−	0.462167i	−0.899365	+	0.437198i	$0.855971\pi$
$774$			3.23195i			0.116170i
$775$	−12.5949	−	14.9870i	−0.452422	−	0.538347i
$776$		−	7.94277i		−	0.285129i
$777$	−14.0071	−	19.1675i	−0.502503	−	0.687632i
$778$	−14.3095	−	14.3095i	−0.513019	−	0.513019i
$779$	−11.2251	−	11.2251i	−0.402179	−	0.402179i
$780$	0.316250	−	7.30678i	0.0113236	−	0.261625i
$781$		−	5.57181i		−	0.199375i
$782$	−8.83049			−0.315778
$783$		−	8.69238i		−	0.310640i
$784$		−	8.23228i		−	0.294010i
$785$	−20.8328	−	0.901679i	−0.743555	−	0.0321823i
$786$	5.13259			0.183074
$787$	−20.2540	+	20.2540i	−0.721978	+	0.721978i	−0.969008	−	0.247030i	$-0.920545\pi$
$787$	−20.2540	+	20.2540i	−0.721978	+	0.721978i	0.247030	+	0.969008i	$0.420545\pi$
$788$	11.8547	−	11.8547i	0.422307	−	0.422307i
$789$			14.1939i			0.505315i
$790$	−0.338023	+	7.80984i	−0.0120263	+	0.277862i
$791$	−21.6709	+	21.6709i	−0.770530	+	0.770530i
$792$			0.350472i			0.0124535i
$793$	4.26454	+	4.26454i	0.151438	+	0.151438i
$794$	−0.498839	+	0.498839i	−0.0177031	+	0.0177031i
$795$	−7.38988	−	8.05851i	−0.262092	−	0.285806i
$796$	−6.76638	−	6.76638i	−0.239828	−	0.239828i
$797$			33.9189i			1.20147i	0.799449	+	0.600734i	$0.205125\pi$
$797$			33.9189i			1.20147i	−0.799449	+	0.600734i	$0.794875\pi$
$798$	7.85360	−	7.85360i	0.278014	−	0.278014i
$799$	−40.7650	+	40.7650i	−1.44216	+	1.44216i
$800$	−4.98130	−	0.432008i	−0.176116	−	0.0152738i
$801$	−3.03601	+	3.03601i	−0.107272	+	0.107272i
$802$	10.8582	+	10.8582i	0.383417	+	0.383417i
$803$	0.349795	+	0.349795i	0.0123440	+	0.0123440i
$804$	−15.0146			−0.529525
$805$	−0.471091	+	10.8843i	−0.0166038	+	0.383621i
$806$	9.05520	−	9.05520i	0.318956	−	0.318956i
$807$	−14.1250	−	14.1250i	−0.497224	−	0.497224i
$808$	0.514124			0.0180868
$809$	−11.7103	−	11.7103i	−0.411713	−	0.411713i	0.470622	−	0.882335i	$-0.344030\pi$
$809$	−11.7103	−	11.7103i	−0.411713	−	0.411713i	−0.882335	+	0.470622i	$0.844030\pi$
$810$	−1.64803	+	1.51129i	−0.0579059	+	0.0531013i
$811$	12.1269			0.425834			0.212917	−	0.977070i	$-0.431704\pi$
$811$	12.1269			0.425834			0.212917	+	0.977070i	$0.431704\pi$
$812$	33.9251			1.19054
$813$	−7.81863	+	7.81863i	−0.274211	+	0.274211i
$814$	−1.72122	+	1.25783i	−0.0603288	+	0.0440867i
$815$	10.5810	+	11.5384i	0.370637	+	0.404172i
$816$	5.00185	−	5.00185i	0.175100	−	0.175100i
$817$	−6.50356	−	6.50356i	−0.227531	−	0.227531i
$818$	7.92408	−	7.92408i	0.277059	−	0.277059i
$819$	9.02641	−	9.02641i	0.315408	−	0.315408i
$820$	−9.19321	+	8.43043i	−0.321041	+	0.294403i
$821$	29.1034			1.01571			0.507857	−	0.861441i	$-0.330438\pi$
$821$	29.1034			1.01571			0.507857	+	0.861441i	$0.330438\pi$
$822$	17.7222			0.618134
$823$	−17.5087	−	17.5087i	−0.610316	−	0.610316i	0.332712	−	0.943028i	$-0.392036\pi$
$823$	−17.5087	−	17.5087i	−0.610316	−	0.610316i	−0.943028	+	0.332712i	$0.892036\pi$
$824$			9.07861i			0.316268i
$825$	−1.34153	+	1.12741i	−0.0467062	+	0.0392514i
$826$	−58.6196			−2.03964
$827$	−14.9493			−0.519837			−0.259918	−	0.965631i	$-0.583696\pi$
$827$	−14.9493			−0.519837			−0.259918	+	0.965631i	$0.583696\pi$
$828$	1.24836			0.0433834
$829$	−8.25148	−	8.25148i	−0.286586	−	0.286586i	0.549143	−	0.835729i	$-0.314954\pi$
$829$	−8.25148	−	8.25148i	−0.286586	−	0.286586i	−0.835729	+	0.549143i	$0.814954\pi$
$830$	−33.5186	−	1.45074i	−1.16345	−	0.0503560i
$831$	17.2915	+	17.2915i	0.599834	+	0.599834i
$832$		−	3.27075i		−	0.113393i
$833$			58.2326i			2.01764i
$834$	2.59247	+	2.59247i	0.0897699	+	0.0897699i
$835$	22.2187	+	24.2290i	0.768909	+	0.838479i
$836$	−0.705244	−	0.705244i	−0.0243914	−	0.0243914i
$837$	−3.91530			−0.135333
$838$	−13.1368			−0.453803
$839$	−12.0705			−0.416720			−0.208360	−	0.978052i	$-0.566813\pi$
$839$	−12.0705			−0.416720			−0.208360	+	0.978052i	$0.566813\pi$
$840$	−5.89834	−	6.43202i	−0.203512	−	0.221926i
$841$			46.5575i			1.60543i
$842$	10.6585	+	10.6585i	0.367315	+	0.367315i
$843$	10.2385			0.352631
$844$	9.92928			0.341780
$845$	−3.47927	−	3.79407i	−0.119691	−	0.130520i
$846$	5.76291	−	5.76291i	0.198133	−	0.198133i
$847$	30.0181	−	30.0181i	1.03143	−	1.03143i
$848$	−3.45760	−	3.45760i	−0.118734	−	0.118734i
$849$	−21.3584	+	21.3584i	−0.733019	+	0.733019i
$850$	35.2362	+	3.05589i	1.20859	+	0.104816i
$851$	4.48029	+	6.13088i	0.153582	+	0.210164i
$852$	11.2416	−	11.2416i	0.385131	−	0.385131i
$853$	−55.2308			−1.89107			−0.945533	−	0.325527i	$-0.894458\pi$
$853$	−55.2308			−1.89107			−0.945533	+	0.325527i	$0.894458\pi$
$854$	7.19651			0.246259
$855$	0.275159	−	6.35741i	0.00941025	−	0.217419i
$856$	−1.33354	−	1.33354i	−0.0455796	−	0.0455796i
$857$	42.6736			1.45770			0.728851	−	0.684672i	$-0.240054\pi$
$857$	42.6736			1.45770			0.728851	+	0.684672i	$0.240054\pi$
$858$	−0.810561	−	0.810561i	−0.0276721	−	0.0276721i
$859$	37.8772	−	37.8772i	1.29235	−	1.29235i	0.359028	−	0.933327i	$-0.383108\pi$
$859$	37.8772	−	37.8772i	1.29235	−	1.29235i	0.933327	−	0.359028i	$-0.116892\pi$
$860$	−5.32635	+	4.88441i	−0.181627	+	0.166557i
$861$	−21.7713			−0.741964
$862$	−13.6585	−	13.6585i	−0.465210	−	0.465210i
$863$	27.1162	+	27.1162i	0.923047	+	0.923047i	0.997244	−	0.0741970i	$-0.0236394\pi$
$863$	27.1162	+	27.1162i	0.923047	+	0.923047i	−0.0741970	+	0.997244i	$0.523639\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	9.47812	+	0.410229i	0.322266	+	0.0139482i
$866$	16.2196	−	16.2196i	0.551166	−	0.551166i
$867$	−23.3607	+	23.3607i	−0.793371	+	0.793371i
$868$		−	15.2809i		−	0.518666i
$869$	0.866367	+	0.866367i	0.0293895	+	0.0293895i
$870$	14.3253	−	13.1367i	0.485674	−	0.445376i
$871$	34.7254	−	34.7254i	1.17662	−	1.17662i
$872$	−2.30925	−	2.30925i	−0.0782011	−	0.0782011i
$873$		−	7.94277i		−	0.268822i
$874$	−2.51203	+	2.51203i	−0.0849708	+	0.0849708i
$875$	5.64641	−	43.2684i	0.190884	−	1.46274i
$876$			1.41148i			0.0476895i
$877$	3.65778	−	3.65778i	0.123514	−	0.123514i	−0.642648	−	0.766162i	$-0.722164\pi$
$877$	3.65778	−	3.65778i	0.123514	−	0.123514i	0.766162	+	0.642648i	$0.222164\pi$
$878$	−4.52525	+	4.52525i	−0.152720	+	0.152720i
$879$	0.874366			0.0294916
$880$	−0.577588	+	0.529665i	−0.0194705	+	0.0178550i
$881$			35.1647i			1.18473i	0.805670	+	0.592364i	$0.201805\pi$
$881$			35.1647i			1.18473i	−0.805670	+	0.592364i	$0.798195\pi$
$882$		−	8.23228i		−	0.277195i
$883$	28.4200			0.956410			0.478205	−	0.878248i	$-0.341288\pi$
$883$	28.4200			0.956410			0.478205	+	0.878248i	$0.341288\pi$
$884$			23.1363i			0.778157i
$885$	−24.7529	+	22.6991i	−0.832059	+	0.763021i
$886$	−17.5292	−	17.5292i	−0.588906	−	0.588906i
$887$	30.2121	+	30.2121i	1.01442	+	1.01442i	0.999894	+	0.0145284i	$0.00462470\pi$
$887$	30.2121	+	30.2121i	1.01442	+	1.01442i	0.0145284	+	0.999894i	$0.495375\pi$
$888$	−6.01048	−	0.934944i	−0.201699	−	0.0313747i
$889$			80.8160i			2.71048i
$890$	−9.59172	−	0.415146i	−0.321515	−	0.0139157i
$891$			0.350472i			0.0117413i
$892$	6.49659	+	6.49659i	0.217522	+	0.217522i
$893$			23.1931i			0.776126i
$894$	−11.9807	+	11.9807i	−0.400695	+	0.400695i
$895$	1.31599	−	30.4053i	0.0439889	−	1.01634i
$896$	−2.75974	−	2.75974i	−0.0921963	−	0.0921963i
$897$	−2.88717	+	2.88717i	−0.0963997	+	0.0963997i
$898$	24.1689	+	24.1689i	0.806528	+	0.806528i
$899$	34.0333			1.13508
$900$	−4.98130	−	0.432008i	−0.166043	−	0.0144003i
$901$	24.4580	+	24.4580i	0.814813	+	0.814813i
$902$			1.95504i			0.0650957i
$903$	−12.6138			−0.419762
$904$			7.85255i			0.261172i
$905$	−21.2907	−	23.2171i	−0.707726	−	0.771761i
$906$	−7.63344	+	7.63344i	−0.253604	+	0.253604i
$907$	−13.2909			−0.441317			−0.220658	−	0.975351i	$-0.570821\pi$
$907$	−13.2909			−0.441317			−0.220658	+	0.975351i	$0.570821\pi$
$908$	16.6142			0.551363
$909$	0.514124			0.0170524
$910$	28.5173	+	1.23428i	0.945340	+	0.0409159i
$911$	−31.5562	−	31.5562i	−1.04550	−	1.04550i	−0.998914	−	0.0465896i	$-0.985165\pi$
$911$	−31.5562	−	31.5562i	−1.04550	−	1.04550i	−0.0465896	−	0.998914i	$-0.514835\pi$
$912$		−	2.84578i		−	0.0942332i
$913$	−3.71831	+	3.71831i	−0.123058	+	0.123058i
$914$		−	15.3091i		−	0.506381i
$915$	3.03882	−	2.78668i	0.100460	−	0.0921248i
$916$			2.86631i			0.0947056i
$917$			20.0318i			0.661507i
$918$	5.00185	−	5.00185i	0.165086	−	0.165086i
$919$	−1.91721	−	1.91721i	−0.0632431	−	0.0632431i	0.674778	−	0.738021i	$-0.264239\pi$
$919$	−1.91721	−	1.91721i	−0.0632431	−	0.0632431i	−0.738021	+	0.674778i	$0.764239\pi$
$920$	1.88663	+	2.05733i	0.0622004	+	0.0678282i
$921$	−12.1034			−0.398821
$922$	−19.6061	+	19.6061i	−0.645691	+	0.645691i
$923$			51.9984i			1.71155i
$924$	−1.36784			−0.0449987
$925$	−15.7560	−	26.0144i	−0.518053	−	0.855349i
$926$	25.4617			0.836724
$927$			9.07861i			0.298181i
$928$	6.14644	−	6.14644i	0.201767	−	0.201767i
$929$	53.6670			1.76076			0.880378	−	0.474273i	$-0.157289\pi$
$929$	53.6670			1.76076			0.880378	+	0.474273i	$0.157289\pi$
$930$	−5.91716	−	6.45254i	−0.194031	−	0.211587i
$931$	16.5656	+	16.5656i	0.542915	+	0.542915i
$932$	−8.37425	+	8.37425i	−0.274308	+	0.274308i
$933$			10.0122i			0.327783i
$934$			18.9252i			0.619250i
$935$	4.08568	−	3.74668i	0.133616	−	0.122530i
$936$		−	3.27075i		−	0.106908i
$937$	18.7194	−	18.7194i	0.611538	−	0.611538i	−0.331809	−	0.943347i	$-0.607659\pi$
$937$	18.7194	−	18.7194i	0.611538	−	0.611538i	0.943347	+	0.331809i	$0.107659\pi$
$938$		−	58.5999i		−	1.91335i
$939$	15.4515	+	15.4515i	0.504242	+	0.504242i
$940$	18.2069	+	0.788024i	0.593843	+	0.0257025i
$941$	12.7400			0.415313			0.207657	−	0.978202i	$-0.433416\pi$
$941$	12.7400			0.415313			0.207657	+	0.978202i	$0.433416\pi$
$942$	−9.32544			−0.303839
$943$	6.96372			0.226770
$944$	−10.6205	+	10.6205i	−0.345668	+	0.345668i
$945$	−5.89834	−	6.43202i	−0.191873	−	0.209234i
$946$			1.13271i			0.0368275i
$947$	−13.4498			−0.437059			−0.218529	−	0.975830i	$-0.570126\pi$
$947$	−13.4498			−0.437059			−0.218529	+	0.975830i	$0.570126\pi$
$948$			3.49594i			0.113543i
$949$	−3.26443	−	3.26443i	−0.105968	−	0.105968i
$950$	10.8930	−	9.15441i	0.353417	−	0.297008i
$951$	−27.0220			−0.876248
$952$	19.5215	+	19.5215i	0.632695	+	0.632695i
$953$	0.709621	−	0.709621i	0.0229869	−	0.0229869i	−0.695520	−	0.718507i	$-0.744826\pi$
$953$	0.709621	−	0.709621i	0.0229869	−	0.0229869i	0.718507	+	0.695520i	$0.244826\pi$
$954$	−3.45760	−	3.45760i	−0.111944	−	0.111944i
$955$	0.289468	−	6.68799i	0.00936696	−	0.216418i
$956$	−16.9584	+	16.9584i	−0.548475	+	0.548475i
$957$		−	3.04644i		−	0.0984773i
$958$	3.00653	+	3.00653i	0.0971366	+	0.0971366i
$959$			69.1674i			2.23353i
$960$	−2.23398	−	0.0966903i	−0.0721013	−	0.00312067i
$961$			15.6704i			0.505496i
$962$	16.0632	−	11.7386i	0.517898	−	0.378466i
$963$	−1.33354	−	1.33354i	−0.0429729	−	0.0429729i
$964$	−9.32818	−	9.32818i	−0.300441	−	0.300441i
$965$	−34.2582	+	31.4158i	−1.10281	+	1.01131i
$966$			4.87216i			0.156759i
$967$	−4.89161			−0.157304			−0.0786519	−	0.996902i	$-0.525062\pi$
$967$	−4.89161			−0.157304			−0.0786519	+	0.996902i	$0.525062\pi$
$968$		−	10.8772i		−	0.349605i
$969$			20.1302i			0.646674i
$970$	13.0899	−	12.0038i	0.420292	−	0.385419i
$971$	−50.8953			−1.63331			−0.816654	−	0.577128i	$-0.804173\pi$
$971$	−50.8953			−1.63331			−0.816654	+	0.577128i	$0.804173\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−10.1180	+	10.1180i	−0.324369	+	0.324369i
$974$		−	42.0200i		−	1.34641i
$975$	12.5197	−	10.5215i	0.400953	−	0.336957i
$976$	1.30384	−	1.30384i	0.0417349	−	0.0417349i
$977$			56.6245i			1.81158i	0.423727	+	0.905790i	$0.360721\pi$
$977$			56.6245i			1.81158i	−0.423727	+	0.905790i	$0.639279\pi$
$978$	4.95068	+	4.95068i	0.158305	+	0.158305i
$979$	−1.06404	+	1.06404i	−0.0340067	+	0.0340067i
$980$	13.5670	−	12.4414i	0.433383	−	0.397425i
$981$	−2.30925	−	2.30925i	−0.0737287	−	0.0737287i
$982$			14.2813i			0.455735i
$983$	−38.4422	+	38.4422i	−1.22612	+	1.22612i	−0.260694	+	0.965422i	$0.583951\pi$
$983$	−38.4422	+	38.4422i	−1.22612	+	1.22612i	−0.965422	+	0.260694i	$0.916049\pi$
$984$	−3.94446	+	3.94446i	−0.125745	+	0.125745i
$985$	37.4529	+	1.62102i	1.19335	+	0.0516501i
$986$	−43.4780	+	43.4780i	−1.38462	+	1.38462i
$987$	22.4918	+	22.4918i	0.715922	+	0.715922i
$988$	6.58164	+	6.58164i	0.209390	+	0.209390i
$989$	4.03463			0.128294
$990$	−0.577588	+	0.529665i	−0.0183570	+	0.0168338i
$991$	−32.4216	+	32.4216i	−1.02991	+	1.02991i	−0.0303674	+	0.999539i	$0.509668\pi$
$991$	−32.4216	+	32.4216i	−1.02991	+	1.02991i	−0.999539	+	0.0303674i	$0.990332\pi$
$992$	−2.76854	−	2.76854i	−0.0879012	−	0.0879012i
$993$	−4.02257			−0.127652
$994$	43.8743	+	43.8743i	1.39161	+	1.39161i
$995$	0.925240	−	21.3772i	0.0293321	−	0.677702i
$996$	−15.0040			−0.475420
$997$	−6.92720			−0.219387			−0.109693	−	0.993965i	$-0.534987\pi$
$997$	−6.92720			−0.219387			−0.109693	+	0.993965i	$0.534987\pi$
$998$	4.58214	−	4.58214i	0.145045	−	0.145045i
$999$	−6.01048	−	0.934944i	−0.190163	−	0.0295803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.a.43.1	✓	36
5.2	odd	4		1110.2.o.a.487.18	yes	36
37.31	odd	4		1110.2.o.a.253.18	yes	36
185.142	even	4	inner	1110.2.l.a.697.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.1	✓	36	1.1	even	1	trivial
1110.2.l.a.697.1	yes	36	185.142	even	4	inner
1110.2.o.a.253.18	yes	36	37.31	odd	4
1110.2.o.a.487.18	yes	36	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-1.51129 - 1.64803i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000i q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} -0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075i q^{13} +(2.75974 + 2.75974i) q^{14} +(2.23398 + 0.0966903i) q^{15} +1.00000 q^{16} -7.07368 q^{17} +1.00000 q^{18} +(-2.01227 + 2.01227i) q^{19} +(1.51129 + 1.64803i) q^{20} +3.90286i q^{21} +0.350472 q^{22} -1.24836i q^{23} +(0.707107 + 0.707107i) q^{24} +(-0.432008 + 4.98130i) q^{25} -3.27075 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.75974 + 2.75974i) q^{28} +(-6.14644 - 6.14644i) q^{29} +(-0.0966903 + 2.23398i) q^{30} +(-2.76854 + 2.76854i) q^{31} +1.00000i q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-8.71889 - 0.377368i) q^{35} +1.00000i q^{36} +(-4.91116 + 3.58895i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(-2.31277 - 2.31277i) q^{39} +(-1.64803 + 1.51129i) q^{40} +5.57830i q^{41} -3.90286 q^{42} +3.23195i q^{43} +0.350472i q^{44} +(-1.64803 + 1.51129i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.23228i q^{49} +(-4.98130 - 0.432008i) q^{50} +(5.00185 - 5.00185i) q^{51} -3.27075i q^{52} +(-3.45760 - 3.45760i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(-0.577588 + 0.529665i) q^{55} +(-2.75974 - 2.75974i) q^{56} -2.84578i q^{57} +(6.14644 - 6.14644i) q^{58} +(-10.6205 + 10.6205i) q^{59} +(-2.23398 - 0.0966903i) q^{60} +(1.30384 - 1.30384i) q^{61} +(-2.76854 - 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} -1.00000 q^{64} +(5.39030 - 4.94305i) q^{65} +(-0.247821 + 0.247821i) q^{66} +(-10.6169 - 10.6169i) q^{67} +7.07368 q^{68} +(0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} -1.00000 q^{72} +(-0.998067 + 0.998067i) q^{73} +(-3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 - 2.01227i) q^{76} +(-0.967210 - 0.967210i) q^{77} +(2.31277 - 2.31277i) q^{78} +(-2.47200 + 2.47200i) q^{79} +(-1.51129 - 1.64803i) q^{80} -1.00000 q^{81} -5.57830 q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(10.6904 + 11.6576i) q^{85} -3.23195 q^{86} +8.69238 q^{87} -0.350472 q^{88} +(-3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 + 9.02641i) q^{91} +1.24836i q^{92} -3.91530i q^{93} +(5.76291 + 5.76291i) q^{94} +(6.35741 + 0.275159i) q^{95} +(-0.707107 - 0.707107i) q^{96} +7.94277 q^{97} +8.23228 q^{98} -0.350472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{4} + 4 q^{7}+O(q^{10}) \) 36 * q - 36 * q^4 + 4 * q^7	\( 36 q - 36 q^{4} + 4 q^{7} - 4 q^{10} + 4 q^{14} + 36 q^{16} - 32 q^{17} + 36 q^{18} + 4 q^{19} + 8 q^{22} - 4 q^{25} + 8 q^{26} - 4 q^{28} + 36 q^{29} - 4 q^{31} + 4 q^{33} - 12 q^{35} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 4 q^{40} - 16 q^{42} + 4 q^{45} + 16 q^{47} - 16 q^{50} - 8 q^{53} + 16 q^{55} - 4 q^{56} - 36 q^{58} - 4 q^{59} - 4 q^{61} - 4 q^{62} - 4 q^{63} - 36 q^{64} + 52 q^{65} - 4 q^{66} + 16 q^{67} + 32 q^{68} - 8 q^{69} - 28 q^{70} - 8 q^{71} - 36 q^{72} - 4 q^{73} + 28 q^{74} + 16 q^{75} - 4 q^{76} + 8 q^{77} - 4 q^{78} - 12 q^{79} - 36 q^{81} - 8 q^{82} + 8 q^{83} + 8 q^{85} + 32 q^{86} - 8 q^{87} - 8 q^{88} - 24 q^{89} + 56 q^{91} + 16 q^{94} - 20 q^{95} + 40 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^4 + 4 * q^7 - 4 * q^10 + 4 * q^14 + 36 * q^16 - 32 * q^17 + 36 * q^18 + 4 * q^19 + 8 * q^22 - 4 * q^25 + 8 * q^26 - 4 * q^28 + 36 * q^29 - 4 * q^31 + 4 * q^33 - 12 * q^35 - 4 * q^37 + 4 * q^38 + 4 * q^39 + 4 * q^40 - 16 * q^42 + 4 * q^45 + 16 * q^47 - 16 * q^50 - 8 * q^53 + 16 * q^55 - 4 * q^56 - 36 * q^58 - 4 * q^59 - 4 * q^61 - 4 * q^62 - 4 * q^63 - 36 * q^64 + 52 * q^65 - 4 * q^66 + 16 * q^67 + 32 * q^68 - 8 * q^69 - 28 * q^70 - 8 * q^71 - 36 * q^72 - 4 * q^73 + 28 * q^74 + 16 * q^75 - 4 * q^76 + 8 * q^77 - 4 * q^78 - 12 * q^79 - 36 * q^81 - 8 * q^82 + 8 * q^83 + 8 * q^85 + 32 * q^86 - 8 * q^87 - 8 * q^88 - 24 * q^89 + 56 * q^91 + 16 * q^94 - 20 * q^95 + 40 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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